(?, ?)-Zb-Geraghty type contraction in b-metric-like spaces via b-simulation function

Abstract

The aim of this paper is to introduce the notion of (?, ?)-Zb-Geraghty type contraction via b-simulation function and use this contraction to establish a common fixed point theorem for a pair of self-mappings in the context of a b-metric-like space. Our result extends and generalizes the result of Matthews [21], Khojasteh et al. [20], Demma et al. [15], Chandok [12] and some others also. We deduce some corollaries from our main result and provide examples to illustrate our results. Moreover, we apply our result to obtain a solution of second order differential equation.